Let's remember one thing. No matter what you connect, it's being upconverted. Even if you connect a first generation DVD player with composite to your HDTV, the TV _will_ upconvert the signal to whatever the TV's native resolution is. The question is exactly how that upconversion is performed.
Chances are the chip in your Gateway screen can do a pretty good job. It might or might not be better than software based upconversion, but that can only be told by testing. Chances are, you won't notice much of a difference. 480p from a good anamorphic 16x9 DVD can be surprisingly good if processed well. Old 16x9 or (gasp) 2.35:1 letterboxed to 4x3 movies (which have less than 300 lines of real resolution in some cases) won't look good no matter what you use to process them.
Some high end DVD players or dedicated scalers / processors can do some real nifty magic to upconvert content to a higher resolution, but the fact remains that you can't magically re-create details. It's pretty impressive what can be done with a basic setup on your PC using ffdshow + avisynth in real time to lanczos or spline resize to your screen resolution, and add some noise.
Yes, I said add noise. It tricks your eyes into seeing more details!! It does _not_ compare by any means (to good eyes anyway) to HD-DVD or BluRay of course, but that's not the point.
Spending money on an upconverting DVD player (that's not absurdly high end) and connecting it to your monitor seems like a waste of money to me, unless you really really like the look of one's processor. Just buy a new DVD burner, and watch your movies on your PC, and let software scaling or your monitor's hardware scaler do the job for you, whatever you prefer
~MiSfit